WATER and CLOTH simulation
What you want to achieve is coupling, where two physics simulations interact with each other. Unfortunately, Blender does not support this and can only, like you have said, run the individual simulations. You could try this, but note that the results won't be accurate:

Run the cloth simulation, maybe with some settings that make it look like it is floating in water (lower gravity, more air resistance)
After baking the cloth simulation (this is important), give the cloth object fluid physics and set to effector.
Run the fluid simulation.

Though this may produce some realistic results, it will look fake after closer analysis. This is because the fluid reacts to the movement of the cloth, but the cloth does not react to the fluid. There are some simulation programs that do support these physics interactions, most notably Houdini FX. Unfortunately, nearly all of those softwares will cost money.